Thicker eggshells are not predicted by host egg ejection behaviour in four species of Australian cuckoo

Defences of hosts against brood parasitic cuckoos include detection and ejection of cuckoo eggs from the nest. Ejection behaviour often involves puncturing the cuckoo egg, which is predicted to drive the evolution of thicker eggshells in cuckoos that parasitise such hosts. Here we test this prediction in four Australian cuckoo species and their hosts, using Hall-effect magnetic-inference to directly estimate eggshell thickness in parasitised clutches. In Australia, hosts that build cup-shaped nests are generally adept at ejecting cuckoo eggs, whereas hosts that build dome-shaped nests mostly accept foreign eggs. We analysed two datasets: a small sample of hosts with known egg ejection rates and a broader sample of hosts where egg ejection behaviour was inferred based on nest type (dome or cup). Contrary to predictions, cuckoos that exploit dome-nesting hosts (acceptor hosts) had significantly thicker eggshells relative to their hosts than cuckoos that exploit cup-nesting hosts (ejector hosts). No difference in eggshell thicknesses was observed in the smaller sample of hosts with known egg ejection rates, probably due to lack of power. Overall cuckoo eggshell thickness did not deviate from the expected avian relationship between eggshell thickness and egg length estimated from 74 bird species. Our results do not support the hypothesis that thicker eggshells have evolved in response to host ejection behaviour in Australian cuckoos, but are consistent with the hypothesis that thicker eggshells have evolved to reduce the risk of breakage when eggs are dropped into dome nests.

Main Menu > Active Batch > Configuration Target Ball Size: 1,5 mm Data logging mode: Auto Logging Rate: 10 / sec (7) Check calibration is correct Main Menu > Active Batch > Calibration Target Ball Size: 1,5 mm Calibration Mode: Zero + 3Points (8) All 4 calibration points should have an "X" in the box to the right under 'CAL', if they do not the probe needs to be re-calibrated: Zero: zero calibration cap for 1.5mm ball Calibration Mode > Zero > *OK* Place 1.5mm ball in cap Place cap (with ball) onto probe, let go and wait until a reading appears Lift cap (with ball) at least 3cm from probe, then place back onto probe Repeat until n = 5 Press *OK* to save calibration (9) Place cradle and plastic protector over probe and tighten screw until the cradle is stable and the protector is taut over the probe point (10) Measure and record the protector thickness

Data collection
(1) In MSoft 7, double-click MiniTest USB Adapter (130886)  (6) Press *OK* on the base unit to begin data logging, press *OK* on the base unit to stop N.B. if you click OK on the screen instead of the base unit to stop the data logging MSoft 7 will freeze and the data will be lost If looking for specific n value, watch the number column in the direct import window until it reaches the necessary n value (7) When ready to save readings, click *OK* on direct import window (8) Navigate to the correct file location, rename the file based on the specimen number and measurement, then confirm the file is saving in the correct format (.ms7) (e.g. E12345_APEX) (9) The direct import window will close, and the new file will be visible under the File Explorer window, clicking that file will activate and display it in the Preview window (where Statistics, Histogram & Trend diagram can be viewed) (10) To take another batch of readings simply click Direct Import again to reopen the window and repeat the process -it is wise to log all the batch readings for each specimen before exporting the files to Excel in groups (11) To export readings to Excel (necessary to correct calculations for protector thickness) click Excel document while the active batch is selected (12) Navigate to the correct file location, confirm the file is correctly named based on the specimen number and measurement being taken and change the file extension to the correct format (.xls NOT .xlsx or .csv) (13) Excel spreadsheet will automatically open (but this can be ignored for now) (14) Always copy & save MSoft 7 and Excel files from the laptop to a USB

Manual handling
(1) Check whether blowhole is large enough to fit 1.5 mm ball without damage, and for jagged edges as a sign of weakness/propensity to crack (2) Candle eggs Check which end is the base and which is the apex -the base will be apparent by the appearance of a darker circle where the membrane air pocket was located Check for fractures and membrane issues -any hairline fractures or thin patches will show as lighter and membrane or other biological material will show as darker (3) Note: If the blowhole is too small, jagged, or there are visible issues when candling, the egg is at risk of damage and should not be measured (4) Weigh the egg (5) Photograph the egg (6) Gently place 1.5 mm ball into egg through blowhole (7) Gently bring the egg to the probe point with the conical end of the egg pointing down (8) Leave egg to balance (do not touch while measuring) with the most conical point touching the probe (9) Take roughly n = 50 (10) Gently move egg over probe point until ball is adjacent to the blowhole at the centre line of the egg, with the blowhole on the far side of the probe point from the person measuring. Always hold the egg with the conical apex end to the right of the person measuring. Slowly and smoothly rotate the egg, moving the blowhole away from the person measuring (in an anticlockwise direction) until the blowhole is adjacent to the measurer on the near side of the probe -it is best to use a hand-over-hand technique when rotating to prevent jerky movements of the egg. Note that the time (and n value) will vary with the size of the egg for this measurement Figure S1. Steps in measuring the thickness of museum eggshell specimens. Thickness was directly estimated using Hall-effect magnetic-inference with an ElectroPhysik MiniTest FH7200 gauge, an FH4 magnetic probe and a 1.5 mm diameter steel ball at a rate of 10 measurements per second and an accuracy of ± 3 µm + 1% of the reading.

Data processing
(1) Open the .xls file for the batch of interest in Excel and navigate to the 'Readings (Total)' sheet (2) Insert a new column between Reading and Unit (right-click column C header > Insert) (3) Name the new column "corrected for protector" (4) Enter equation to subtract mean protector calibration previously calculated from values in Reading column (5) Place mouse over bottom-left corner of cell until the cursor turns into a solid black cross (+), click and drag down to last row of the Reading column (6) Use the functions in Excel to calculate the following statistics: Mean + (1.5*IQR) CX = the last row of the Reading column -this will vary with the number of data points in the batch (n) The equations in column 2 of the table above can be copies & pasted into Excel, but will all show as "#NAME?" until CX is changed to an actual cell value The coefficient of variation is calculated as a percentage using the following equation: = # ̅ ' ( * 100% Figure S2. Frequency histogram showing egg breakage occurrence during magnetic thickness measurement. Most eggs were not damaged by manual handling and measurement (grey bars; 57 of 61 eggs undamaged; 93.4%). Three breakages were observed in eggs weighing < 0.06 g which had no pre-existing damage (blue bar). The only breakage that occurred in a relatively large egg was a single specimen with a pre-existing hair-line fracture (orange bar).

R code for repeatability analysis
Please see the DataDryad package for R inputs.  Figure S3. Eggshell morphology of cuckoos (orange) and their hosts (blue). Eggshell thickness was measured at two points on the egg: (A) Eggshell thickness at the meridian of the egg, which is the circumference around the widest part of the egg. (B) Eggshell mass. (C) Eggshell thickness at the apex of the egg, which is the most conical end opposite the air sac.

Apex
(D) Eggshell length from apex to the blunt end of the egg. The total distribution is displayed untransformed as block dots. Box plots are the median, interquartile range (Q1 -Q3) and range (min -max). Figure S4. Normalisation of eggshell thickness measurements. Egg size (using mass as a proxy), is not a strong predictor of normalised eggshell thickness. For both (A) meridian and (B) apex measurements, the slope approaches zero (0.0024 -0.0027) and the R 2 is low (0.15 -0.17). This indicates that raw eggshell thickness was successfully normalised by dividing eggshell thickness by egg length.